Elected officials are not government employees. It is not, in fact, turtles all the way down. They may be paid by the government, but the government does not dictate when they get hired and fired. It's possible that someone may be both an elected official and a government employee, but that's fairly rare (something like: Congressman and member of the military reserve, in which case they're only a government employee while activated).
Elected officials set policies. Government employees implement those broad policies into action. You can change the policies your representative is pushing by changing the representative. I'm a little unclear on where exactly the FBI director falls (because he's appointed to his job with the advice and consent of the Senate, which makes a difference for these things, maybe). A FBI field office head chanting "locker up" in a press conference would be violation though, yes.
The IRS disagrees, but obviously different legal contexts have different definitions, but I am aware of none supporting the distinction you are trying to make.
Example: Hatch Act provides that persons below the policy-making level in the executive branch of the federal government must not only refrain from political practices that would be illegal for any citizen, but must abstain from "any active part" in political campaigns.
In Garcetti v. Ceballos, the Supreme Court held “that when public employees make statements pursuant to their official duties, the employees are not speaking as citizens for First Amendment purposes, and the Constitution does not insulate their communications from employer discipline.”
Obviously, speech and debate clause controls for Federal Congress members.
